Pedigree analysis is a widely used statistical method for fitting genetic models and doing linkage analysis. It is used for determining the mode of inheritance of trait or if the trait is linked to a marker. In using the method, likelihoods are computed and maximized numerically on the computer. I have developed a computer package PAP (Pedigree Analysis Package) for doing these analyses. This grant application proposes to develop new genetic models and methodology for use in PAP. Several of the genetic models to be developed are mixed models. One is an autosomal/X-linked mixed model for discriminating between those two modes of inheritance. The others are variations on the major gene/polygenic mixed model used to determine if a major locus is segregating for some trait. I previously derived an approximation to the likelihood of the mixed model on quantitative phenotypic data. Similar approximations will be derived for use on dichotomous and bivariate phenotypic data. Loss of information in an analysis is sometimes necessary for practical reasons. One example of this is linkage analysis to a multi-allelic marker. computer space and time limitations prohibit inclusion of all possible genotypes in the model. If all pedigree members have been typed and linkage equilibrium is assumed, the marker can be reduced to four alleles without loss of information. If either one of these conditions is not met, the genetic model must be reduced. Another situation in which information is often lost to allow completion of an analysis is when the pedigree structure contains loops. Again computer space ant time limitations may prohibit their inclusion, with subsequent loss of information. In both cases, methodology will be developed to allow successful completion of the analysis without loss of information. Recursive computation of first and second derivatives of the likelihood have been shown to be theoretically possible. Also, common-sib environment and assortative mating can theoretically be included in the models of which the likelihood is computed. The application of these two theoretical results will be attempted.